Oleh: M. Zaki Riyanto dan Sri Wahyuni (Jurusan Matematika FMIPA UGM)

Abstract: Let  F[{x_1},...,{x_n}] be a polynomial ring with variables  {x_1},...,{x_n} over a field F. Suppose I is an ideal of  F[{x_1},...,{x_n}]. A subset  S \subset F[{x_1},...,{x_n}] is said to be a basis for I if it’s finitely generated by S. Fix a monomial order relation. We denote by LT(f) the leading term of  f \in F[{x_1},...,{x_n}] and LT(I) the set of all leading term of all elements in I. A subset  \lbrace {g_1},...,{g_t} \rbrace \subset F[{x_1},...,{x_n}] is said to be Grobner basis for I if \left \langle LT(I)  \right \rangle = \left \langle LT(g_1),...,LT(g_t) \right \rangle. In this paper we discussed the motivation of construction of the Grobner basis and a method to find the Grobner basis using Buchberger Algorithm.

Kata Kunci: Buchberger Algorithm, Grobner Basis, Ideal, Monomial Ordering, Polynomial Ring.

(Makalah ini telah dipresentasikan pada Seminar Nasional Matematika HPA (Himpunan Peminat Aljabar) di UIN Syarif Hidayatullah, Jakarta pada tanggal 27 Maret 2010)


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